For an hour and 20 minutes the two men politely discussed "The nature of human beings and the question of their ultimate origin" touching on the meaning of consciousness, the evolution of human language – and Dr Williams’s beard.

For much of the discussion the Archbishop sat quietly listening to Prof Dawkins’s explanations of human evolution.

At one point he told the professor that he was “inspired” by “elegance” of the professor’s explanation for the origins of life – and agreed with much of it.

Prof Dawkins told him: “What I can’t understand is why you can’t see the extraordinary beauty of the idea that life started from nothing – that is such a staggering, elegant, beautiful thing, why would you want to clutter it up with something so messy as a God?”

Dr Williams replied that he “entirely agreed” with the “beauty” of Prof Dawkins’s argument but added: “I’m not talking about God as an extra who you shoehorn on to that.”

There was surprise when Prof Dawkins acknowledged that he was less than 100 per cent certain of his conviction that there is no creator.

The philosopher Sir Anthony Kenny, who chaired the discussion, interjected: “Why don’t you call yourself an agnostic?” Prof Dawkins answered that he did.

An incredulous Sir Anthony replied: “You are described as the world’s most famous atheist.”

Prof Dawkins said that he was “6.9 out of seven” sure of his beliefs.

“I think the probability of a supernatural creator existing is very very low,” he added.

He also said that he believed it was highly likely that there was life on other planets.

At one point he discussion strayed onto the theoretical question of whether a traditional cut throat razor could be described as a more complicated thing than an electric shaver.

There was laughter as the Archbishop said he would attempt an answer before adding: “Not that I know much about razors.”

During a wide-ranging discussion the Archbishop also said that he believed that human beings had evolved from non-human ancestors but were nevertheless “in the image of God”.

He also said that the explanation for the creation of the world in the Book of Genesis could not be taken literally.

“The writers of the Bible, inspired as I believe they were, they were nonetheless not inspired to do 21st Century physics,” he said.

When Prof Dawkins suggested that he believed the Pope took a rather more literal interpretation of the origins of humans, the Archbishop joked: “I will ask him some time.”